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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 8670.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8670.a1 | 8670a1 | \([1, 1, 0, -48, 288]\) | \(-43713001/116640\) | \(-33708960\) | \([]\) | \(2160\) | \(0.13192\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 8670.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 8670.a do not have complex multiplication.Modular form 8670.2.a.a
sage: E.q_eigenform(10)